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1.3 Overview

In chapter 2, I consider modeling and inference for ordinal outcomes nested within
categorical responses. I propose a mixture of normal distributions for latent vari-
ables associated with the ordinal data. This mixture model allows us to fix without
loss of generality the cutpoint parameters that link the latent variable with the ob-
served ordinal outcome. Moreover, the mixture model is shown to be more flexible
in estimating cell probabilities when compared to the traditional Bayesian ordinal
probit regression model with random cutpoint parameters. I extend the model to
account for possible dependence among the outcomes in different categories. I apply
the model to a randomized phase III study to compare treatments on the basis of
toxicities recorded by type of toxicity and grade within type. The data include the
different (categorical) toxicity types exhibited in each patient. Each type of toxicity
has an (ordinal) grade associated to it. The dependence among the different types
of toxicity exhibited by the same patient is modeled by introducing patient-specific
random effects.

In chapter 3, I discuss inference for a human phage display experiment with three
stages. The data are tripeptide counts by tissue and stage. The primary aim of the
experiment is to identify ligands that bind with high affinity to a given tissue. I for-
malize the research question as inference about the monotonicity of mean counts over
stages. The inference goal is then to identify a list of peptide-tissue pairs with signif-
icant increase over stages. I develop a semi-parametric model as a mixture of Poisson
distributions with a Dirichlet process prior on the mixing measure. The posterior
distribution under this model allows the desired inference about the monotonicity of
mean counts. However, the desired inference summary as a list peptide-tissue pairs
with significant increase involves a massive multiplicity problem. I consider two al-
ternative approaches to address this multiplicity issue. First I propose an approach
based on the control of the posterior expected false discovery rate. I notice that the
implied solution ignores the relative size of the increase. This motivates a second

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